   SEARCH HOME Math Central Quandaries & Queries  Question from prateet, a student: in an equilateral triangle prove that the centroid and centre of the circumcircle coincide here i am not clear about the concept of centroid and circumcircle i cant understand how AGis 2/3 AD. please help in details about the topic mentioned. Prateet,

You can look in our glossary for a definition of the centroid of a triangle and circumcentre of a triangle. You have an equilateral triangle and the symmetry in this triangle is very useful in working with the centroid and circumcircle. In my diagram L, M and N are the midpoints of the respective sides. C is the centroid. To show it in the circumcentre you need to show that |CP| = |CQ| = |CR|.

By the symmetry the line segment RN bisects the angle QRP. What is the measure of angle NRP? Again by the symmetry the 6 angles at C have the same measure. What is the measure of the angle MCR? What does this tell you about the triangle MCR?

Does this help?

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Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.